Course Information

MATH348: Advanced Engineering Mathematics - Introduction to partial differential equations, with applications to physical phenomena. Fourier series. Linear algebra, with emphasis on sets of simultaneous equations. Prerequisite: MATH 225 or equivalent.

Instructor Information

Instructor : Scott Strong

Office : Chauvenet Hall 266

Office Phone : 303.384.2446

email : math348@gmail.com

Textbook Information

The bookstore sells an abridged version of the following text. The abridged version contains the seven chapters and an appendix:

1. Chapter 5: Power Series Solutions to ODE and Frobenius method

2. Chapter 7: Systems of Linear Algebraic Equations

3. Chapter 8: Eigenvalues and Eigenvectors

4. Chapter 11: Fourier Series

5. Chapter 12: Introduction to Linear Partial Differential Equations

6. Chapter 20: Numerical Methods in Linear Algebra

7. Chapter 21: Numerical Methods in Differential Equations

While this will meet out needs, if you plan to continue in mathematics for a minor or area of special interest or seek an advanced degree in your field then you are advised to get the unabridged edition. Older editions are fine and relatively cheap from online retailers.

Course Materials

The following outlines materials specific to this course. The materials, as indicated, have been developed over time and have achieved a steady-state. An archive of older ticc pages is available. There is also a binder available in the library of practically everything ever done since Fall 2006. The ticc websites pick up at Spring 2008 when I started presenting linear algebra first.

Syllabus

Lecture Slides

There are various lecture slides associated with the course. They were developed during the Spring of 2010 and are intended to deliver important bulk concepts while avoiding the desire to write down 'every little thing.' Specifically, the slides address:

1. Definitions that are not useful for me to write and students to rewrite during lecture.

2. Derivations that will never need to be reproduced but need to be communicated quickly because they lead to important consequences.

3. Derivations that will need to be reproduced and have been recorded for clarity.

Listed in each slide set are:

   Associated Section/Pages from EK.AEM
   Associated Lecture Notes
   Associated Homework Assignments

• MATH 348 : Advanced Engineering Mathematics - Lecture Slides

Lecture Notes

There is a set of lecture notes associated with the course. They were developed during the Fall of 2008 through the Spring of 2009 and are intended to outline key-points, objectives and goals from the text in the order we cover them. Listed in each set are:

   Associated Sections/Pages from EK.AEM
   Suggested Problems from EK.AEM
   Brief Outline of Lecture Talking Points
   Lecture Objectives
   Lecture Goals  

• MATH 348 : Advanced Engineering Mathematics - Lecture Notes

Assignments

Students learn by doing problems. Consequently, a course's assignments are critically important and is where the majority of student learning takes place. So, this raises an important question, "how should the assignments for a course like AEM be structured?" This is a tough question and to arrive at my 'answer,' we need some background.

First, while the majority of students (>90%) in AEM are engineers their skill-sets are highly inhomogeneous. Specifically, you have all had two-years of post-secondary mathematics at different difficulty levels, pace and success. So, there isn't a standard assumption I can use about what you have seen, how well you remember it and, most importantly, how comfortable you are manipulating "it." Moreover, it is unclear where you are going from here. Some of you will find yourself in industry and some in academia, which means that your needs from the material are different. Clearly, any line of best fit through the material will be poor.

Second, everyone in this course needs to understand that they have an fairly extensive mathematical background. Seriously, how many students do you know that will have had six semesters of course work, outside of their discipline, when they graduate? Those that do are typically awarded a minor in the field. The point is, you are moving past plug-and-chug mathematics and into the conceptual framework of finite and infinite dimensional linear theory. Finally, we address the question

      How should the assignments for a course like AEM be structured?

Based on the diverse background of the student audience and the growing sophistication of the material homework, assignments should be constructed to highlight both the algorithmic procedures and conceptual framework of linear mathematics. For quick practice skills the recommended homework problems and examples in the text should suffice. However, a student should only do this after replicating the work from class and deciding they wish to have more practice.

On the other hand, the homework assignments are made to provide a deeper understanding of the course material and often take the student past a first-calculation and into a deeper concept. For example, using the power-series representation for the exponential function is a first-calculation, while using this power-series to show the deep connection between exponential functions and sinusoids is uses multiple pieces of math to arrive at a deeper concept. All students should be able to handle the first-calculations in the homework and at the same time the more advanced students are still challenged by the deeper concepts present in many of the problems. This is the goal of the homework assignments.

Homework Assignments

The assignments for this course have reached a steady-state. Consequently, solutions are often available through students who have taken the course in the past. Since these resources might not be available to all students, I have drafted a set of solutions to these homework assignments which I make available through this site. These solutions were, more or less, finalized during the Spring of 2010 and represents the end of an evolution starting around 2006. Outside of the lecture itself, these homeworks and solutions represents some of the oldest parts of the course and many of the ancestors can be found on older ticc pages .

In the past the homeworks tended to have a good deal of discussion providing context to a problem so that both the mechanics and concepts could be gleaned. However, after talking with some students and course reviews I decided to move the commentary to the solutions in favor of a more streamlined problem statement. It is unclear whether this latest incarnation is 'better' than the past but what is clear is that they won't be regressing unless someone else wants to revamp them. If you want to see the previous versions then visit the older ticc pages . If you find any typos in these solutions then I would appreciate you letting me know. They are pretty clean but they could always be `cleaner.'

With that said, I must make emphasize the following point:

     Caveat Emptor : We will work from these problems and since solutions are 
     readily available it is up to the individual user to make sure that they 
     are LEARNING the material. If you buy into a program of procrastination 
     followed by rapid and thoughtless re-creation then you may find yourself with an
     inadequate product that cannot be returned. 

• MATH 348 : Advanced Engineering Mathematics - Assignments

Exams

Previous exams going back through Fall2008 and review sheets are available for studying via the following link.

• MATH 348 : Advanced Engineering Mathematics - Exams

Supplemental Materials

• MATH 348 : Advanced Engineering Mathematics - Supplemental Materials
• MATH 348 : Advanced Engineering Mathematics - Archive